Classifying foliations

Details Classifying foliations Classifying foliations

2008-04-08

arxiv.org/abs/0804.1240v2

Mathematics

Dynamical Systems

Revisions are changes indicated by referee, and reformat for AMS style: Contemp. Math. Proceedings

Scientific paper

We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and discussed, including expansion rate, local entropy, and orbit growth rates. This leads to a decomposition of the foliated space into Borel or measurable components with these various dynamical types. The dynamical structure is compared with the classification via secondary classes.

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